My old battery was old, and would barely start my jeep. I went to firestone and got a new one, but after installing it there was no power. All of the connections were good, so I gave it a jump. As soon as I started driving around, the check gauges light came on and the battery voltage was maxed out at 19. I parked the car and turned it off, and the battery was dead again.

Cables can rot from the inside, and look fine on the outside. Test them to see if there is resistance. between teh cables, alt and battery, one bad leg of that triangle can cause the others to die in a swift manner.

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Voltage does not make the battery in this case.
Amps are where it's at
Take it back to FS, have them charge the battery and perform a 'load test'.
IMHO: Wal-Mart has better batteries.
I see your MCBH. Are you a Marine?
LG

I brought the alternator in and it tested good. I used a wire brush on all the connections and I still didnt get anything. I tried to jump it again, to see if the voltage was really at 19+ when it was running. All that happened was I got power when the cables were connected, but when I tried to start it I lost all power and couldnt get it back. Im going to go out tomorrow and check the resistance between the cables.

Perform routine maintenance of the start and charge systems. Remove, clean, and firmly reconnect all the wires and cables to the battery, starter, and alternator. Look for corroded or damaged cables or connectors and replace as needed. Copper wires should be copper color, not black or green. Do the same for the grounding wires from the starter to engine block, the ground wires at the coil, and the ground wires from the battery and engine to the Jeep's frame/body. You must remove, wire brush, and clean until shiny the cable/wire ends and whatever they bolt to.

Jeeps do not tolerate low voltage, bad connections, or poor grounds.

Place your DVOM (Digital Volt Ohm Multi-Meter) on the 20 volt scale. First check battery voltage by placing your multi-meter's positive lead on the battery's positive post ( the actual post, not the clamp ) and the negative lead on the negative post. You need a minimum of 12 volts to continue testing. Next, leave your meter connected and take a reading while the engine is cranking. Record this voltage reading. Now connect your positive lead to the battery terminal stud on the starter and the negative lead to the starter housing. Again, crank the engine and record the voltage reading. If the voltage reading at the starter is not within 1 volt of battery voltage then you have excessive voltage drop in the starter circuit.

I started doing resistance test on the main battery cables. Everything is at a good 0 ohms, except one line goes up to 300-400 ohms. Im not sure if thats bad or not.

Also when I connect the battery, I still get no power to anything, and the negative terminal get really hot. The positive one stays cold. Could that be an issue with the starter? I am going to attempt to take the starter off tomorrow and bring it in, along with the battery.